While the stock was down in the morning, it fell further after the Wall Street Journal first reported that the talks between the two sides had broken down. Reuters confirmed the news.
Novartis may attempt to pursue a deal for Cytokinetics in the future or a different suitor may acquire the company, the person said.
Reuters could not immediately ascertain the reason for the breakdown in the talks.
On Monday, Reuters reported that Novartis is in the lead to acquire Cytokinetics, ahead of other bidders that include AstraZeneca and Johnson & Johnson.
Both Novartis and Cytokinetics said they do not comment on market rumors and speculation.
Shares of Cytokinetics, which has a market capitalization of nearly $10 billion as of Wednesday's closing price, have more than doubled in value since Oct. 31, when reports of the company attracting takeover interests first surfaced.
In an interview with CNBC on Tuesday, Novartis CEO Vasant Narasimhan had said the company's overall M&A strategy was focused on smaller acquisitions, involving assets valued below $5 billion.
Cytokinetics' stock has dropped 6% in the last two sessions since Narasimhan's comments on fears that a deal with Novartis may not happen.
Truist Securities analyst Srikripa Devarakonda in a note said she sees Cytokinetics as an attractive acquisition target as late-stage trial data of the company's key experimental drug, aficamten, supports its potential to be best in its class.
The company is testing aficamten for treatment of hypertrophic cardiomyopathy (HCM), an inherited chronic heart disease that can cause cardiac arrest.
(Reporting by Leroy Leo in Bengaluru and Emma-Victoria Farr; Editing by Shailesh Kuber and Maju Samuel)
